Design: Blocked RCT, with 3 levels, and randomization done at level 1 (individual level).

Models: random treatment effects.

Power Validation

  • M = 3
  • J = 20
  • K = 10
  • rho: \(\rho\) = 0.5
  • ATE ES = 0.125, 0.125, 0.125
  • R2: \(R^2_1\) = 0.1, 0.1, 0.1, \(R^2_2\) = 0.1, 0.1, 0.1, \(R^2_3\) = 0.1, 0.1, 0.1
  • ICC: \(\text{ICC}_2\) = 0.2, 0.2, 0.2, \(\text{ICC}_3\) = 0.2, 0.2, 0.2
  • Omega: \(\omega_2\) = 0.1, \(\omega_3\) = 0.1

Varying school size

\(\bar{n}\) = 100

\(\bar{n}\) = 75

\(\bar{n}\) = 50

Varying R2

\(R^2_1 =\) 0.6, 0.6, 0.6

\(R^2_2 =\) 0.6, 0.6, 0.6

\(R^2_3 =\) 0.6, 0.6, 0.6

\(R^2_1 =\) 0, 0, 0 \(R^2_2 =\) 0, 0, 0 \(R^2_3 =\) 0, 0, 0

Varying rho

\(\rho =\) 0.2

\(\rho =\) 0.8

Varying true positives

ATE (ES) = 0.125, 0, 0

Varying ICC

\(\text{ICC}_2\) = 0.7, 0.7, 0.7

\(\text{ICC}_3\) = 0.7, 0.7, 0.7

Varying Omega

\(\omega_2\) = 0.8, \(\omega_3\) = 0.1

\(\omega_2\) = 0.1, \(\omega_3\) = 0.8

\(\omega_2\) = 0.8, \(\omega_3\) = 0.8

MDES validation

## 
## 
## +------------+---------------+-------------+-------------+
## |    MTP     | Adjusted MDES | Indiv Power | Target MDES |
## +============+===============+=============+=============+
## |    rawp    |     0.125     |    0.613    |    0.125    |
## +------------+---------------+-------------+-------------+
## | Bonferroni |     0.124     |    0.338    |    0.125    |
## +------------+---------------+-------------+-------------+
## |     BH     |     0.125     |    0.507    |    0.125    |
## +------------+---------------+-------------+-------------+
## |    Holm    |     0.125     |    0.436    |    0.125    |
## +------------+---------------+-------------+-------------+
## 
## Table: blocked_i1_3r

Sample size validation

## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      K      |     10      |     0.504     |         10         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      K      |     11      |     0.437     |         10         |
## +------+-------------+-------------+---------------+--------------------+
## |  BH  |    nbar     |     NA      |      NA       |         50         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |    nbar     |     NA      |      NA       |         50         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_i1_3r